Question

An ideal gas has a molar specific heat Cp= 5R/2. The gas is kept in a closed vessel of volume 0.0083 m3 at a temperature of 300K and a pressure of 1.6 × 106 Nm-2.
If 2.49 × 104 Joules of heat energy is supplied to the gas, calculate the final temperature and the pressure of the gas.

Answer 1

Explanation:

As here volume of gas remains constant, we have

(ΔQ)v=μCvΔT

Here, Cv=CP−R(5/2)R−R=(3/2)R

μ=PVRT=1.5×106×8.3×10−38.3×300=163

2.49×104=163×32×8.3ΔT

i.e., ΔT=375 or T2−T1=375, i.e., T2=(375+300)

Now as for a given mass of an ideal gas at constant volume,

P∝T

(P2/P1)=(T1/T2)

P2=675300×1.6×106=3.6×106N/m2

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